Suppose you want to know the temperature of a room in degrees celcius. You only have a thermometer which tells you the temperature in fahrenheit. How would you find what the temperature in degrees celcius using this thermometer?
What if you wanted to measure the length of a path in metres but only had a tape measure measuring in feet and inches?
How would you find out what a bag of sweets costs in pounds if you bought them in on holiday in America using US dollars?
All these questions can be answered using a principle known as Direct Proportionality.
If the ratio between two variables (such as pounds and dollars) is always the same then these variables are said to be Directly Proportionalto each other.
Look at the image to the right >>>>
How does it demonstrate direct proportionality?
Can you see any other physical examples around you,
what are they and what makes them directional proportional?
Some worked examples: (taken from ncetm)
Direct proportion problems can be solved by calculating the ratio between two variables...
Potatoes cost 50p per kilogram.
You buy 6 kg so you pay £3.
If you buy 20 kg, you pay £10.
The ratio 6 : 3 is the same as the ratio 20 : 10, since they both simplify to 2 : 1. The cost of potatoes is DIRECTLY PROPORTIONAL to the amount of potatoes you buy
Direct proportion problems can sometimes be solved by scaling...
In a box of sweets there are 5 toffees for every 2 chocolates.
There are 15 toffees in the box.
How many chocolates are there?
In this problem, the ratio of the number of toffees to the number of chocolates is constant.
The solution can be modelled on a number line.
Toffees and chocolates
5 is multiplied by 3 to make 15 (i.e. scaled up by a factor of 3), so 2 must also be multiplied by 3 to get the answer of 6 chocolates.
We could also think of this as finding a pair of equivalent fractions such that:
frac{5} {2} = frac{15} {}
The number of toffees in a box of sweets is DIRECTLY PROPORTIONAL to the number of chocolates.
Another approach is the unitary method, in which the value of one of the variables is reduced to 1....
A cake recipe for 6 people needs 120 g flour.
How much flour will a cake for 7 people need?6 people need 120 g flour.
1 person needs 120 ÷ 6 = 20 g flour.
7 people need 20 × 7 = 140 g flour.
The amount of flour needed to make a cake is DIRECTLY PROPORTIONAL to the amount of people the cake is made for.
Suppose you want to know the temperature of a room in degrees celcius. You only have a thermometer which tells you the temperature in fahrenheit. How would you find what the temperature in degrees celcius using this thermometer?
What if you wanted to measure the length of a path in metres but only had a tape measure measuring in feet and inches?
How would you find out what a bag of sweets costs in pounds if you bought them in on holiday in America using US dollars?
All these questions can be answered using a principle known as Direct Proportionality.
If the ratio between two variables (such as pounds and dollars) is always the same then these variables are said to be Directly Proportional to each other.
what are they and what makes them directional proportional?
Some worked examples: (taken from ncetm)
Direct proportion problems can be solved by calculating the ratio between two variables...
- Potatoes cost 50p per kilogram.
The ratio 6 : 3 is the same as the ratio 20 : 10, since they both simplify to 2 : 1.You buy 6 kg so you pay £3.
If you buy 20 kg, you pay £10.
The cost of potatoes is DIRECTLY PROPORTIONAL to the amount of potatoes you buy
Direct proportion problems can sometimes be solved by scaling...
There are 15 toffees in the box.
How many chocolates are there?
In this problem, the ratio of the number of toffees to the number of chocolates is constant.
The solution can be modelled on a number line.
5 is multiplied by 3 to make 15 (i.e. scaled up by a factor of 3), so 2 must also be multiplied by 3 to get the answer of 6 chocolates.
We could also think of this as finding a pair of equivalent fractions such that:
The number of toffees in a box of sweets is DIRECTLY PROPORTIONAL to the number of chocolates.
Another approach is the unitary method, in which the value of one of the variables is reduced to 1....
- A cake recipe for 6 people needs 120 g flour.
The amount of flour needed to make a cake is DIRECTLY PROPORTIONAL to the amount of people the cake is made for.How much flour will a cake for 7 people need?6 people need 120 g flour.
1 person needs 120 ÷ 6 = 20 g flour.
7 people need 20 × 7 = 140 g flour.
Links and Resources
- Lesson on Linear Equation Graphs (J Mills-Dadson) _Linear_Graph[1].pptx
- Linear Equations Card Sort Linear Equations Card Sort.pub
- Algebra - Tables, Spreadsheets and GraphsAlgebra.pptx
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